Seki, Founder of Modern Mathematics in Japan

Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of Étienne Bézout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them.The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in 2008. This book is the official record of the conference and includes supplements of collated texts of Seki's original writings with notes in English on these texts.Hikosaburo Komatsu (Professor emeritus, The University of Tokyo), one of the editors, is known for partial differential equations and hyperfunction theory, and for his study on the history of Japanese mathematics. He served as the President of the International Congress of Mathematicians Kyoto 1990.

This is a valuable book with good contributions to the field of history of mathematics. Specialists interested in the life and mathematical contributions of Seki will of course benefit from it, but interested readers will benefit from it also. (Toke Knudsen, MAA Reviews, May, 2015)

Inhalt

Part I Contributed papers .- Seki Takakazu, His Life and Bibliography.- Some Reflections on Main Lines of Mathematical Development.- Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322.- Archimedes in China: Archimedes and His Works in Chinese Literature of the Ming and Qing Dynasties.- The Nine Chapters on the Mathematical Procedures and Liu Hui's Mathematical Theory.- On the Alternative Algorithm of the 7th Problem in the Sea Island Mathematical Canon.- A Comparative Study on Traditional Mathematics of Korea and Japan.- The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models.- The Suanxue Qimeng and Its Influence on Japanese Mathematics.- Power Series Expansions in India Around A. D. 1400.- An Early Japanese Work on Chinese Mathematics in Vietnam: Yoshio Mikami's Study of the Vietnamese Mathematical Treatise Chi Minh Toan Phap .- The Jink ki of Yoshida Mitsuyoshi.- Résumé of Works on Mathematics of Seki Takakazu.- Seki Takakazu's Measuring Process of the Volume of Solids Derived from Spheres.- Seki Takakazu's Method on the Remainder Problem.- Seki Takakazu's Method of Calculating the Volume of Solids of Revolution and His Mathematical Object.- Leibniz's Theory of Elimination and Determinants.- Algebra, Elimination and the Complete Book of Mathematics.- Some Questionsand Observations Around the Mathematics of Seki Takakazu.- Ming Antu and His Power Series Expansions.- Standing on the Shoulders of the Giant Influence of Seki Takakazu on Takebe Katahiro's Mathematical Achievements.- Takebe Katahiro's Algorithms for Finding the Circular Arc Length.- The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei.- Manuscripts in the Edo Period: Preliminary Study on Manuscripts Written by Seki Takakazu.- Influence of European Mathematics on Pre-Meiji Japan.- On Contemporary Mathematics in Vietnam.- Part II Supplements .- Notes on Complete Book of Mathematics Vol. 4: Three Essentials.- Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu.- Seki's Trilogy: Methods of Solving Explicit Problems, Methods of Solving Implicit Problems and Methods of Solving Concealed Problems.- Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu.- Methods of Solving Implicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu.- Methods of Solving Concealed Problems, by Seki Takakazu, collated by Hikosaburo Komatsu.- Notes on Complete Book of Mathematics Vol. 10: Geometry.- Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu.- Seki's Theory of Elimination as Compared with the Others'.